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Three-dimensional strain analysis in physical models of geological structures |
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| Authors: | John Morgan |
| Institution: | Earth Sciences Centre, University of Toronto, Toronto, Ont. M5S 3B1, Canada |
| Abstract: | A method is outlined for calculating three-dimensional finite strain in physical models of geological structures containing passive strain markers. This method makes it possible to determine the three-dimensional strain pattern in models of structures that lack any of the types of symmetry (such as that imparted by cylindrical folding) that simplified calculations in previous work. The strain markers in the new method are in the shape of stubby rectangular prisms or cubes. These form a three-dimensional grid or array occupying each of the active layers in a model (e.g., for a simple two-layer gravitationally unstable system, one grid for the overburden layer and one for the buoyant layer). Each of the grids can be described by positions of three families of “strain marker surfaces”, which are contacts between layers of strain markers. After deformation, the model is serial-sectioned horizontally and the traces of the strain marker surfaces on the sections are digitized. The strain state is calculated at each of several hundred points arranged in a three-dimensional “output grid” extending throughout the mechanically active part of the model. An interpolation procedure is used to estimate the spacing and orientation of the strain marker surfaces in the vicinity of each of the output grid points. The following quantities are determined for each of the three families of strain marker surfaces:
This information is used to generate a parallelepiped representing the strain marker geometry in the neighbourhood of the output grid point. The edges of the parallelepiped are equivalent to the coefficients of the strain matrix, from which the three principal strain magnitudes and orientations are readily derived. |
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